

A164572


Numbers n such that n and n+4 are prime powers.


6



1, 3, 4, 5, 7, 9, 13, 19, 23, 25, 27, 37, 43, 49, 67, 79, 97, 103, 109, 121, 127, 163, 169, 193, 223, 229, 239, 277, 289, 307, 313, 343, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 729, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967, 1009, 1087
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OFFSET

1,2


COMMENTS

Numbers n such that n + (0, 4) is a prime power pair.
A generalization of the cousin primes. The cousin primes are a subsequence.
n + (0, 2m), m >= 1, being an admissible pattern for prime pairs, since (0, 2m) = (0, 0) (mod 2), has high density.
n + (0, 2m1), m >= 1, being a nonadmissible pattern for prime pairs, since (0, 2m1) = (0, 1) (mod 2), has low density [the only possible pairs are (2^a  2m1, 2^a) or (2^a, 2^a + 2m1), a >= 0.]


LINKS

Daniel Forgues, Table of n, a(n) for n = 1..1256


PROG

(PARI) is(n)=if(n==1, return(1)); isprimepower(n) && isprimepower(n+4) \\ Charles R Greathouse IV, Apr 24 2015


CROSSREFS

Cf. A006549 Numbers n such that n and n+1 are prime powers.
Cf. A023200, A000961.
Cf. A120431 Numbers n such that n and n+2 are prime powers.
Cf. A164571 Numbers n such that n and n+3 are prime powers.
Cf. A164572 Numbers n such that n and n+4 are prime powers.
Cf. A164573 Numbers n such that n and n+5 are prime powers.
Cf. A164574 Numbers n such that n and n+6 are prime powers.
Sequence in context: A226918 A227391 A209721 * A067530 A259796 A082922
Adjacent sequences: A164569 A164570 A164571 * A164573 A164574 A164575


KEYWORD

nonn


AUTHOR

Daniel Forgues, Aug 16 2009, Aug 17 2009


STATUS

approved



